We build upon the CA model that was validated through the simulation of the Spetses wildfire in Greece in 1990 , to generate the data sets used for training and testing our DL surrogate model. This CA model utilizes square meshes to simulate the stochastic spatial spread of wildfires in a computationally efficient way. By dividing a two-dimensional terrain into 3 × 3 grids, the model allows fire propagation in eight possible directions determined by evaluating the state of a central cell based on the states of its neighbouring cells . The accuracy of the model when fire suppression strategies were included was validated by using the 2014 Dumai forest fire over a 14 d period .

Our CA model incorporates local environmental parameters such as forest information, vegetation density, slope, and meteorological data such as wind speed and wind direction to simulate fire dynamics. Training datasets were derived from three recent fires in California. Various firebreak placement scenarios were evaluated to assess their impact on fire spread. Specifically, we implemented new states in the CA model to represent permanent and temporary firebreaks. For temporary firebreaks, we developed an approach that encodes their remaining duration, allowing the model to track their effectiveness over time. The states of each cell within the grid evolve through discrete time steps as follows:

State 1. The cell contains no fuel and cannot burn.

The transition between CA states evolves over time (Fig. ), and the cells that are either non-burnable (State 1) or have already burned (State 4) do not change state. Burnable cells (State 2) have a probability Pburn of igniting if one or more of their neighbouring cells are burning. Fire spreads to adjacent cells through stochastic transitions from State 2 to State 3, with the ignition probability determined by a probabilistic rule defined in Eq. (): 1Pburn=ph1+pveg1+pdenpspw, where ph denotes the base burning probability, while pveg, pden, ps, and pw correspond to local environmental factors such as vegetation density, canopy cover, slope, wind speed and wind direction, respectively. These parameters are sourced from the IFTDSS . The influence of slope on fire spread is modelled following , with the slope effect ps given as: 2ps=exp⁡aθs, where a is a dimensionless constant, and the slope angle θs is calculated using the following expressions: 3θs=tan⁡-1E1-E2l,for adjacent cellstan⁡-1E1-E22l,for diagonal cells Here, E1 and E2 denote the elevations of the respective cells, and l represents the cell length. The wind effect is modelled following the method proposed in , where: 4pw=exp⁡c1Vwexp⁡Vwc2cos⁡θw-1. Vw represents the wind speed in meters per second, and θw is the angle between the wind direction and the potential fire spread direction (Eq. ). The coefficients c1 and c2 are tunable parameters that modulate the wind's effect on fire propagation . Wind data, including both speed and direction, were taken from . Wind conditions were assumed to be spatially constant over a 27 km × 27 km grid, and the burned area state were resized to 128 × 128 pixels. Each CA simulation time step corresponds to approximately 6 h . This simplification was adopted to constrain the dimensionality of the training space in this proof-of-concept study.

The operational parameters ph, a, c1, and c2 significantly influence fire spread predictions. In , these values are calibrated as follows: ph=0.58,a=0.078,c1=0.045,c2=0.131. These values are derived by minimizing a cost function that fits observed fire spread data from specific wildfire events, and are used as initial values in the parameter identification process. Finally, burning cells (State 3) transit to a burned state (State 4) with a fixed probability Rburned_down = 0.4 throughout the entire simulation.

Our CA model incorporates both temporary and permanent firebreaks. Temporary firebreaks are flexible in their placement and provide complete fire suppression for a limited duration of 10 time steps, equivalent to approximately 3 d (with each time step representing 6 h in real time). In contrast, permanent firebreaks require a minimum distance of 1 km (equivalent to 5 pixels in the CA model) from the fire front and offer a suppression rate of about 90 % . Both types of firebreaks are subject to resource constraints, limiting their maximum extent (in our model that is limited to 50 pixels for each type of firebreak).

For cells affected by a permanent firebreak (State 5), the suppression rate (Rpfb) is 90 %. The probability that a cell under the influence of a permanent firebreak will still burn, Ppfb_burn, is given by: 5Ppfb_burn=1-RpfbPburn, where Pburn is the standard burning probability, calculated using Eq. ().

Temporary firebreaks (States 15 to 6) are assumed to provide 100 % fire suppression for an effective period of approximately 3 d. In the CA simulator, these temporary firebreaks provide complete (100 %) suppression throughout their effective duration of 10 time steps, after which they revert to their original state, allowing fire spread to resume if conditions permit.

The training data set generated by the CA simulator (Fig. ) uses data from each landscape: “Chimney 2016”, “Ferguson 2018”, and “Bear 2020”. Each dataset was generated with random wind directions, randomly positioned fire ignition field, three temporal firebreaks and one permanent firebreak positioned around the ignition field and the CA model simulates fire propagation for 26 time steps, approximately 7 d in real time. Firefighting strategies typically involve placing firebreaks along the active fire front to slow or stop the spread. However, due to the unpredictable and often rapid progression of wildfires, it is not always possible to deploy firebreaks in optimal locations. In our study, we used randomly positioned firebreaks to evaluate whether the DL model can still accurately predict fire propagation under less controlled conditions.

We construct a DL surrogate model trained exclusively on datasets generated by the CA simulations. By learning from the CA model's outputs, the DL model captures the underlying spatio-temporal dynamics and serves as a data-driven approximation of the CA-based wildfire propagation process with significantly improved computational efficiency by leveraging GPU acceleration.

RNNs, a subclass of DL models, are highly suitable for capturing complex temporal patterns. However, encoding inputs into low-dimensional representations could distort essential spatial details. The ConvLSTM architecture, introduced by , addresses this by integrating Convolutional Neural Network and LSTM components into a unified model, and thus effectively retaining spatial information while simultaneously modelling temporal dynamics. This design optimizes computational efficiency by leveraging parameter sharing and sparse connectivity.

In the ConvLSTM framework, the input, forget, and output gates, as well as the cell states, are represented as 3-dimensional tensors. The state update mechanism employs convolution operations, thereby maintaining the spatial structure of the data. The equations governing these processes are: 6it=σWxi⊗xt+Whi⊗zt+bi,ft=σWxf⊗xt+Whf⊗zt+bf,ot=σWxo⊗xt+Who⊗zt+bo,C̃t=tanh⁡Wxs⊗xt+Whs⊗zt+bs,Ct+1=ft⊙Ct+it⊙C̃t,zt+1=ot⊙tanh⁡(Ct+1), where xt∈RN×M denotes burnt area at time t that is generated by the CA simulator and used as the model input. This image represents a wildfire-affected area in an N × M grid format, enhanced with data from human interactions. Each pixel in xt can assume any value from the set S. zt+1∈RN×M represents the model's output at time t+1, serving as a hidden state feature matrix that predicts the next frame of wildfire progression. Similar to xt, each pixel of zt+1 can assume any value from the set S. ⊗ denotes the convolution operation, σ denotes the sigmoid activation function, and tanh⁡ is the hyperbolic tangent function. The variables it, ft, and ot correspond to the input, forget, and output gates, respectively, which regulate the information flow within the memory cell. The term C̃t represents the candidate cell state, Ct is the current cell state, and zt is the hidden state or output of the ConvLSTM cell. Convolutional kernels Wxi, Wxf, Wxo, and Wxs are applied to the input feature landscape xt, while kernels Whi, Whf, Who, and Whs are applied to the previous hidden state zt. The bias terms bi, bf, bo, and bs are associated with the input, forget, output gates, and cell state candidate, respectively. For brevity, the prediction length is set to one time step in Eq. ().

Our ConvLSTM model is designed for a 3-to-3 prediction task, as outlined in Algorithm . To simplify processing, the burned area data are resized to 128 × 128 pixels. The model takes three consecutive 128 × 128 matrices as input, each representing a time step in the fire progression sequence. These matrices encode fire dynamics based on the state definitions of the ConvLSTM model.

The state definitions differ slightly from those in the CA model. Using this multi-class approach, we identify both burning cells and track the duration of temporary firebreaks. The states are defined as follows:

State 0. Unburned cells

The difference in state numbering between the CA simulator and the ConvLSTM model (Table ) arises from their distinct modelling objectives. The CA simulator employs a more detailed state representation (States 1–15) to explicitly track physical fire processes and firebreak degradation. In contrast, the ConvLSTM surrogate model adopts a simplified and compact state encoding (States 0–12) to reduce the complexity of the multi-class classification task, improve training stability, and focus on the dominant fire and firebreak dynamics relevant for prediction. Temporary firebreaks in both models follow the same binary suppression logic and degrade over ten time steps; however, their numerical labels differ due to this abstraction.

The model is trained using data generated by the CA model. It takes the first three time steps of fire progression, with or without firebreaks, as input and predicts the next three time steps. This 3-to-3 prediction approach is formalized in Eq. (). 7xt-3,xt-2,xt-1⟶ConvLSTMtrainzt,zt+1,zt+2.

The model employs the Cross Entropy loss function to evaluate training performance. In multi-class classification tasks (e.g., State 1 to 16 in this application), Cross Entropy measures the dissimilarity between the predicted probability distribution and the true class distribution, penalizing incorrect classifications more heavily. The model outputs represent the states of each cell, positioning the ConvLSTM model as performing a multi-class classification task at each pixel and time-step. The structure of our model is detailed in Table .

The input tensor has a shape of (b,3,2,N,M), where b represents the batch size and N × M denotes the spatial dimensions of the input field. This structure indicates that we have 3 sequential frames and 2 channels. One channel encodes fire information (a matrix where 0 indicates that the pixel has not been affected by fire, 1 indicates that a pixel is either currently burning or has burned and other is for the firebreak states which is from 2 to 12). The second channel was originally designed to include landscape-related data; however, although such data are available for the selected case studies, the limited number and diversity of landscapes are insufficient to train a single generalized model that can robustly learn across different terrains. Consequently, this channel is zero-filled in the current implementation. As a result, the ConvLSTM models are trained separately for each of the three landscapes used in the CA simulations, making the current approach landscape-specific.

For the ConvLSTM layers, each unit maintains a hidden state and a current state, with 128 feature channels and a sequence length of 3. Thus, the ConvLSTM output tensor has a shape of (b,3,2,128,N,M). After passing through the subsequent 3D convolutional layers, the final output of the model has a shape of (b,3,16,N,M), where the sequence length is 3 (corresponding to 3 consecutive frames) and 16 represents the number of prediction categories (e.g., different fire spread states or fire suppression strategies).

The ConvLSTM model is trained using Cross Entropy Loss on the training dataset for “Chimney 2016”, “Bear 2020”, and “Ferguson 2018” fires (Table ) and validated on a distinct validation dataset using three metrics: Mean Squared Error (MSE), Structural Similarity Index Measure (SSIM), and Relative Prediction Error (RPE).

The MSE measures the average squared difference between the predicted (zt) and observed (xt) values. This metric evaluates the overall prediction accuracy of the model, with a lower MSE value indicating better performance. 8MSEzt,xt=1b∑t=1b||xt-zt||2

The SSIM evaluates the structural similarity between the predicted and true images by considering luminance, contrast, and structural information. It ranges from -1 to 1, where a value close to 1 indicates a high degree of similarity. 9SSIMzt,xt=2μxtμzt+c12sxtzt+c2μxt2+μzt2+c1sxt2+szt2+c2

The RPE is defined as the ratio of mismatched pixels between the predicted and observed fire spread landscapes, relative to the total number of pixels (N × M). This metric provides an intuitive measure of the model’s ability to correctly classify the fire spread. 10RPEzt,xt=#xt≠ztN×M where #{xt≠zt} represent the number of mismatched pixels.

To assess the predictive capabilities and computational performance of our model, several wildfire datasets with different configurations were used to set up four test scenarios: a.

Fire Propagation without Firebreaks: for this test scenario, a random ignition field was selected on the landscape, and fire propagation was simulated by using a CA simulator.

For the three landscapes considered, each model was tested with data derived from four distinct scenarios (Table ): (1) three temporary firebreaks combined with one permanent firebreak (3T1P), (2) three temporary firebreaks (3T), (3) two permanent firebreaks (2P), and (4) no firebreak (None). The testing data were generated using the CA simulator and matched the configurations used during model training.

To evaluate the computational efficiency of our three ConvLSTM models, we compared their efficiency with that of the CA model across varying landscape resolutions. A series of experiments was conducted using simulated wildfires, each running for 150 time steps on landscapes of increasing size (from 128 × 128 to 768 × 768). For each landscape resolution, the runtime to predict three consecutive time steps – corresponding to a single ConvLSTM inference – was recorded. To ensure stability and consistency in the results, the average runtime was computed over the full 150-step simulation period. The goal was to evaluate the models' speed and their ability to handle large-scale landscapes, which is essential for real-world wildfire datasets that require high-resolution simulations to capture intricate spatial details.